Normal mode splitting and mechanical effects of an optical lattice in a ring cavity

A novel regime of atom-cavity physics is explored, arising when large atom samples dispersively interact with high-finesse optical cavities. A stable far-detuned optical lattice of several million rubidium atoms is formed inside an optical ring resonator by coupling equal amounts of laser light to each propagation direction of a longitudinal cavity mode. An adjacent longitudinal mode, detuned by about 3 GHz, is used to perform probe transmission spectroscopy of the system. The atom-cavity coupling for the lattice beams and the probe is dispersive and dissipation results only from the finite photon-storage time. The observation of two well-resolved normal modes demonstrates the regime of strong cooperative coupling. The details of the normal mode spectrum reveal mechanical effects associated with the retroaction of the probe upon the optical lattice.     

Circular modes selection in Yb:YAG laser using an intracavity lens with spherical aberration

The possibility of use of ordinary short-focus lenses with strong spherical aberration for mode selection in a laser resonator is demonstrated. Plano-convex spherical lenses with foci from 2.5 to 10.0 cm placed inside the resonator of the CW laser diode pumped Yb:YAG laser were used to select circular modes of Laguerre-Gauss and Bessel-Gauss type, or to get ring-like, multi-mode off-axis oscillations with variable inner and outer diameters of rings. At the constant pump power mode selection was obtained by shifting an intracavity lens along the resonator axis relative to the Yb:YAG ceramics active element of 1.1 mm thickness. Peaked and hollow multi-ring beams with output power up to 30 mW were produced. Near diffraction free (ndf) propagation of the central part (minimum or maximum) of these beams was observed along distances over 10 m from the resonator output coupler. The mechanisms of mode selection due to spherical aberration in the resonator and ndf propagation of output beams are considered. The possibility of producing radially polarized beams from the laser with an intracavity lens and possible applications of the devised laser scheme are discussed.     

UR90环形非稳腔输出模式特性的数值分析

将ＵＲ９０环形非稳腔引入氧碘化学激光器，对其输出模式进行了数值模拟计算，模拟包括了化学动力学，介质横向流动和物理光学等因素，得到与放大率Ｍ和光轴离截取镜距离ａ等参数相关的近场光强，位相及远场光强分布曲线。     

激光辐照下非稳腔镜变形对激光模式的影响

 分析了正支虚共焦非稳腔中腔镜变形对激光模式的影响，采用时间离散化、快速傅里叶变换（FFT）和有限元分析(FEA)方法解决腔镜变形和激光模式两者之间的耦合问题。计算结果表明，随着激光器工作时间的增加，腔镜温升和变形相应增大，谐振腔模式变差，输出光场相位均匀性变差，呈现散焦现象，输出光束质量下降。实验验证了激光器输出光束质量随出光时间的延长而逐渐变坏。     

Investigation of beam characteristics in toric unstable optical resonator

In this paper the characteristics of the output beam of a toric unstable resonator are investigated. Based on the Fresnel–Kirchhof integral and using numerical methods, the performance of toric unstable resonators is simulated and its output beam characteristics are also evaluated. Geometrical resonator parameters, i.e. Fresnel number and magnification as well as the output coupler diameter, are considered in this investigation. The radial and azimuthal modes of the resonator are calculated and the modal behavior of the resonator is described according to geometrical parameters. The power extraction for each specific laser mode has also been inspected by calculating the finesse factor. Using an iteration mode convergence diagram, the mode discrimination of the resonator is investigated.     

1 W tunable near diffraction limited light from a broad area laser diode in an external cavity with a line width of 1.7 MHz

A novel unstable external cavity for a broad area laser diode is presented. The cavity is based on a V-shaped setup that improves the slow axis beam quality by coupling the internal modes of a gain guided laser diode. The novelty here is the compact unstable resonator design without lenses in direction of the slow axis. For frequency stabilisation and to narrow the line width of the laser diode emission a diffraction grating in a Littrow configuration is used. With this setup up to 1 W of near diffraction limited light with a beam quality of M² ? 1.3 and a line width of 1.7 MHz could be achieved. The external cavity laser was tunable over a range of 35 nm (FWHM) around the center wavelength of 976 nm.     

高功率TEA CO_2激光器非稳腔实验研究

为了提高光束质量、压缩光束发散角,利用现有高功率稳定腔TEA CO2激光器进行了非稳谐振腔的技术改造及激光输出试验,非稳谐振腔采用正分支虚共焦型非稳腔方案。为充分研究谐振腔结构参数及激光振荡模体积对输出能量和光束发散角的影响,共设计加工了包含4种放大率、5种模体积的20组非稳腔腔镜组合。在其它参数都相同的试验条件下,进行了非稳腔镜的单脉冲输出对比试验,得到的最大输出能量为14 J,是原平凹稳定腔的70%,而光束发散角只是原平凹稳定腔的1/4。     

Quasi-monolithic ring resonator for efficient frequency doubling of an external cavity diode laser

A quasi-monolithic second-harmonic-generation ring resonator assembled with miniaturized components is presented. The ring contains a 10-mm-long bulk periodically poled lithium niobate crystal for second-harmonic generation, four plane mirrors and two gradient-index lenses. All parts are mounted on a glass substrate with an overall size of 19.5 mm×8.5 mm×4 mm. As pump source a broad-area laser diode operated in an external resonator with Littrow arrangement is utilized. This external cavity diode laser provides near diffraction limited, narrow-bandwidth emission with an optical output power of 450 mW at a wavelength of 976 nm. Locking of the diode laser emission to the resonance frequency of the ring cavity was achieved by an optical self-injection locking technique. With this setup more than 126 mW of diffraction-limited blue light at 488 nm could be generated. The opto–optical conversion efficiency was 28% and a wall plug efficiency better than 5.5% could be achieved.     

高斯光束与谐振腔基模模式光路谐振匹配的分析与校准

为了降低高斯光束与谐振腔耦合过程中失调量和失配量对基于无源谐振腔测量技术精度的影响, 采用高斯光束变换规律、模式耦合有关理论以及光束传播坐标变换等相关理论, 就失调量和失配量对基模耦合效率的影响分别进行分析和模拟, 并据此给出了一般情况下两个参考量同时存在时基模耦合效率的表达式. 分析表明: 失配量的存在主要影响激光器与谐振腔的耦合效率, 而对高阶模式的激发影响较小, 因此对谐振腔的衰减线型影响较小; 失调量的存在对谐振腔高阶模式的激发起主要作用, 给测量带来严重误差. 该结论为利用腔出射光信号来确定误调参量值的实验方案提供了依据. 因此, 在考虑光源光谱线宽的情况下, 就光源光谱线宽的特性提出两种装调校准方案: 基于法布里-珀罗干涉仪法和基于多维象限探测器探测谐振腔出射光的调节回路, 这将为分析基于无源谐振腔的相关技术测量误差来源以及实现测量系统的高精度装调提供理论指导.     

Investigation of the beam propagation in a pumped laser rod

A method investigating the beam propagation in a pumped laser rod is proposed. In this method, the pumped laser rod in a resonator is evenly divided into N segments along the laser rod axis, and each segment is considered as a small thermal lens with thermal focus length of f. Accordingly, the beam radius distributions in the laser rod for the symmetric and asymmetric resonators are thus calculated, respectively. The beam radius distribution in the whole resonator is also calculated. Moreover, the calculated beam distribution in the whole resonator and in the rod is also described in detail.     

Gain induced stability of active plane-parallel resonators

It has been observed for a plane-parallel resonator with a saturated medium that under certain conditions confined beams mainly concentrated near the axis are present. The experiments have been done with a sealed-off plane-parallel CO₂ laser of one meter length and with an internal diameter of 20 mm. Without gain variations such a system is unstable because of thermal defocussing by the heated gas. But due to sufficiently high gain variations the beam converges nevertheless. Since the gain variation increases with decreasing reflectivity confined beams near the optical axis are only observed at sufficiently low reflectivity. The experiments were done with a totally reflecting mirror and an outcoupling mirror having a reflectivity of, respectively, 90%, 80%, 50%, and 36%. For the high reflectivities the outcoupled beam is mainly concentrated near the edge with irregular density distributions. For the low reflectivity the beam is more or less radially symmetric, concentrated near the axis having decreasing intensity with the distance from the axis. The behaviour can be understood by an analysis in which the constant and quadratic term of the complex propagation constant near the optical axis due to gain variations, dispersion and heat effects are taken into account.     

Hybrid optical resonator type laser proposed for direct coupling into optical fiber

Combining one stable resonator with a concave mirror and a coupling-hole plane mirror, and another unstable resonator having a concave mirror and a convex mirror, a new hybrid optical resonator type laser has been proposed by overlapping the concave mirror as a common one and fitting the convex mirror exactly to the coupling-hole. Using theABCD law, the so-called g-parameters are first found for beam confinement. Then, based on the eigen-equation, the field distribution on the plano-convex mirror is obtained with the g-parameters above. Knowing this field distribution results in an effective transmittanceG _{e e}. Finally, the ratio of the inner convex to outer plane mirror radii can be determined for an optimum coupling in both the limiting cases of homogeneously and inhomogeneously broadened gain media. Some numerical examples will also be given for a CO₂ laser having the proposed hybrid resonator.     

Influence of spatial mode matching in end-pumped solid state lasers

We present investigations on the influence of mode matching on the efficiency of longitudinally pumped solid state lasers. In a theoretical part we enhance an existing model for four level lasers from idealized cylindrical modes to arbitary pump and laser modes in a random relative position thereby neglecting beam deformation due to thermal effects. The theoretical predictions were confirmed experimentally with an end-pumped Nd:YAG rod operated at 1064 nm. To investigate the effect of misalignment on the efficiency we used a Ti-Sapphire pump laser which was displaced relative to the laser beam. To establish the influence of arbitary pump modes on laser performance a diode laser equipped with coupling optics served as pump source for the same resonator. The resulting decrease in slope efficiency compared to the Ti-Sapphire pumped system could be explained in terms of limited mode overlap due to the characteristic pump field distribution produced by the diode coupling optics.     

大口径谐振腔式固体激光中的动力学不稳定性研究

大口径谐振腔式固体激光定标到足够高功率后,由于非稳定腔内激光不对称振荡导致介质上激光强度横向不均匀,激光提取与介质产热耦合会引起激光输出功率和光束质量在时域上的不稳定性。针对三种激光器构型:Nd:YAG薄片、Yb:YAG薄片和浸入式液冷叠片激光器,通过理论分析与数值模拟揭示了其各自不同的光热耦合机制及其影响因素,给出了激光输出的瞬态演化规律。结果表明,前两种构型中基于激光动力学的光热耦合具有饱和效应,其动力学不稳定性只出现在特定参数区间,可以通过恰当的设计加以避免;第三种构型中动力学不稳定性表现出明显的阈值特征,在强光状态下只能通过减少冷却液吸收系数来抑制。     

Frame dragging with optical vortices

General Relativistic calculations in the linear regime have been made for electromagnetic beams of radiation known as optical vortices. These exotic beams of light carry a physical quantity known as optical orbital angular momentum. It is found that when a massive spinning neutral particle is placed along the optical axis, a phenomenon known as inertial frame dragging occurs. Our results are compared with those found previously for a ring laser and an order of magnitude estimate of the laser intensity needed for a precession frequency of 1 Hz is given for these “steady” beams of light.     

Role of optical resonator on the pointing stability of copper vapor laser beam

This paper presents a first comprehensive study on the pointing stability of copper vapor laser with an emphasis on bringing out the role of optical resonator. Long term (∼10 min), single pulse, far-field beam pointing stability of a 5.5 kHz repetition rate copper vapor laser (λ = 510 nm) with plane-plane, unstable and filtering resonators, is studied. It is established that the resonator optics largely decides the CVL pointing stability. Minimum beam pointing angle of 8 μrad from generalized diffraction filtered resonator (GDFR) is obtained in contrast to a maximum value of 120 μrad from the plane-plane resonator. The unstable resonators data is in between. The relative trends in CVL pointing stability are discussed in terms of wave-front distortions due to resonator mode build up from optical noise, thermal and mirror misalignment effects. The degree of optical resonator immunity to phase distortions dictates the net pointing stability achieved.     

输出环状光束的新型激光谐振腔

提出一种输出环状光束的新型激光谐振腔,即在稳定激光谐振腔中采用外环耦合方式得到环状光束的输出。利用For-Li数值迭代算法求解此类激光谐振腔的积分方程,通过计算机编程计算了平面一凹球面稳定谐振腔的输出端平面镜在不同半径的情况下,谐振腔镜面上和衍射耦合输出场基模的振幅和相位分布。计算结果预示了当输出端平面镜半径小于通常的稳定腔的基模半径时,衍射耦合输出场有稳定的环状光束输出。实验中TEA CO2激光器采用印刷电路板预电离结构,增益长度90cm,腔长5m,球面全反射镜曲率半径20m,输出端平面镜半径4．5mm,得到了内环半径为4．5mm、外环半径为5．5mm的基模环形光斑输出。从而在理论上和实验上证实了该方案产生环状光束的可行性。     

Azimuthally polarized 1 kW CO2 laser with a triple-axicon retroreflector optical resonator

An optical resonator for generating high-power, axially symmetric polarized beams is demonstrated. The rear mirror of a commercial CO(2) laser is replaced by a triple-axicon retroreflector unit that is composed of a waxicon and an axicon accurately fitted together. The selection of the polarization is made by the reflectivity difference between p and s polarizations at the inclined surfaces. Sharp discrimination of polarization within a 0.4% of difference in reflectivity is demonstrated. A stable 1 kW azimuthally polarized LG01 laser beam is generated, and the measured beam quality is 2.0.     

Effect of chromatic aberration on Gaussian beams: non-dispersive laser resonators

The propagation of a non-monochromatic (polychromatic) TEM₀₀ Gaussian beam in vacuum, its passage through a thin plate and its transformation by a thin lens are studied in the case of a non-dispersive laser resonator. The basic assumptions of the model are as follows: optical fields are stationary and plane-polarized, the paraxial wave equation is valid, an equivalent non-dispersive hemiconfocal resonator represents the lasing medium and its stable resonator, the laser emits in a single mode. It is also assumed that the plate and the lens have large transverse dimensions. Mathematical expressions, for beam radius, divergence, radius of curvature and beam parameter product, are obtained. A beam quality factor for polychromatic Gaussian beams is defined and its value calculated in each case of interest. It is proposed to simulate a dispersive laser resonator by a non-dispersive resonator complemented with a plate and/or a thin lens.     

大功率TEA CO2激光器非稳腔的设计与实验

相比于传统稳腔高功率TEA CO2激光器,如何在不降低功率的基础上,改善其光束质量一直研究者关心的问题。本文在原有稳腔激光器的基础上,设计了三组望远镜虚共焦腔镜,给出了完整的设计过程并进行了理论分析。同时对不同组的非稳腔激光器进行了对比实验研究,结果表明非稳腔能够在保证高单脉冲能量的基础上极大地改善激光远场发散角,其中最佳腔镜组合能够达到单脉冲能量13.7J,其发散角为1mrad（稳腔为2.4mrad）,激光脉宽50ns（稳腔为98ns）。这就为此种类型激光器应用于激光制造领域奠定了基础。